An adaptive RNN vehicle trajectory tracking controller and control method based on online learning

Abstract

The application discloses an adaptive RNN vehicle trajectory tracking controller and control method based on online learning, introduces a recurrent neural network (RNN) method, fully utilizes the core advantages that the recurrent neural network (RNN) method can capture dynamic change rules in time series, model long-term dependence, has nonlinear mapping capability and network internal feature expression capability, and thus significantly improves the modeling capability of nonlinear coupling relations between complex system states and control inputs. Through the improvement, the application effectively solves the control precision and trajectory tracking performance problems of vehicle dynamics under complex working conditions (such as model mismatch), and exhibits significant superiority in the field of vehicle dynamics control. Through the synergistic effect of the prediction-feedback controller, the system can keep the high efficiency of online prediction control, and realize more accurate and stable path tracking under complex environments.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of automatic driving vehicle trajectory tracking control, and particularly relates to an adaptive RNN trajectory tracking controller and a control method based on online learning. BACKGROUND

[0002] The design of a high-precision and high-reliability trajectory tracking controller under complex road working conditions has always been the focus of the automatic driving industry. Although the model-based control strategy is intuitive and easy to understand, the control law design is highly dependent on the accuracy of the vehicle model, and it is usually difficult to comprehensively describe the complex nonlinear and time-varying dynamics of the vehicle by relying on linearization and simplification assumptions, especially in high-speed or complex road conditions. The control effect is poor in the model mismatch scene.

[0003] Data-driven modeling is considered a promising technology route. The data-driven modeling method provides the ability to directly learn dynamic relationships from data in vehicle trajectory tracking control, and is particularly suitable for handling complex nonlinear and time-varying problems. It provides important support for automatic driving vehicles to achieve high-precision and high-robustness trajectory tracking control in different scenes with lower modeling cost and higher adaptability.

[0004] The traditional offline learning strategy extracts the overall rules and characteristics of the system through a complete data set in the training stage, providing a relatively comprehensive initial knowledge reserve for the model. However, this method also has obvious limitations: first, offline learning requires the collection of a complete training data set covering various working conditions in advance, and the cost of collecting and labeling these data is often high, especially in complex road conditions and extreme conditions, data may be difficult to exhaust all potential scenarios. Second, the offline trained model cannot dynamically adapt to changes in the environment during vehicle operation, such as changes in road friction coefficient, tire performance degradation or the appearance of unknown obstacles, which may lead to insufficient generalization ability of the system and affect the reliability of trajectory tracking. In contrast, the online learning strategy updates model parameters in real time, effectively overcoming the shortcomings of offline learning. Online learning can dynamically adjust the weights and structure of the model according to the current operating state of the vehicle and the environmental conditions, thereby gradually improving the description of the system dynamics. This adaptive ability enables the model to cope with changing road conditions and vehicle states, improving the robustness and adaptability of the system.

[0005] Recurrent Neural Network (RNN) is a neural network model that is good at processing time series data, which can capture the time dependence in the data by introducing hidden states to jointly model the current input and past time step information. The advantage of RNN is that it can effectively learn the long-term dependence characteristics of dynamic systems, and is suitable for describing complex time-varying nonlinear systems. When applied to vehicle trajectory tracking control, the time memory characteristics of RNN enable it to model the nonlinear relationship of vehicle dynamics and predict future states, thereby providing forward-looking decisions in path planning and control. Compared with traditional models, RNN has stronger nonlinear expression ability and adaptability to dynamic environment, which helps to improve the accuracy and robustness of trajectory tracking, especially in complex working conditions and unknown environment.

[0006] Kalman filter is a recursive algorithm widely used in state estimation of dynamic systems, which combines system model and measurement data to achieve optimal state prediction and update in noisy environment. In the prediction stage, Kalman filter uses the system dynamic equation to predict the current state and its uncertainty based on the state and control input at the last time; in the update stage, the sensor measurement and the predicted value are fused to correct the state estimation and dynamically adjust the confidence of the system. This algorithm can capture the dynamic changes of the system in real time, and is particularly suitable for state estimation in trajectory tracking control, improving the prediction accuracy and robustness of the system. SUMMARY

[0007] To solve the problems in the background art and achieve high-precision trajectory tracking control, the present application proposes an online learning adaptive RNN controller and control method, which combines the advantages of RNN time sequence memory characteristics, Kalman filter adaptive update ability and feature expansion nonlinear expression ability, etc. In the online learning mechanism, the actual running state of the vehicle is continuously collected and fed back to adapt to the dynamic changes of the vehicle dynamics in real time, and the internal weights of the RNN neural network are gradually updated and adjusted, thereby improving the modeling accuracy of the nonlinear dynamic relationship of the vehicle dynamics system. In addition, the present application also introduces a double PID feedback controller to provide more accurate real-time error correction for the vehicle. The model mismatch of the vehicle in complex working conditions can still achieve high-quality trajectory tracking control.

[0008] The technical solution of the present application is: an adaptive RNN vehicle trajectory tracking control method based on online learning, comprising the following steps:

[0009] s1: based on the nonlinear mapping relationship of the vehicle The state equation is constructed to describe the vehicle dynamics. Wherein X represents the state vector of the system, which contains the vehicle lateral velocity v y and yaw rate ω, and u represents the control input, i.e. front wheel steering angle δ fMeanwhile, the mapping relationship is discretized.

[0010] s2: At each time step, the network receives the predicted value of the state variable at the previous time The longitudinal vehicle speed v at the current time x,t And the current control input of the system δ f,t And normalized by the activation function.

[0011] s3: Construct the characteristic polynomial ε t,i Indicates that the i-th layer network at time t is composed of the state variable current longitudinal vehicle speed v x,t , the lateral speed predicted at the previous time The yaw rate predicted at the previous time And the front wheel steering angle δ at the current time f Finally, a high-dimensional feature vector ε is constructed by different pointer combinations t The dimension of the feature vector is the number of RNN network layers.

[0012] s4: Based on the high-dimensional feature vector, construct the observation matrix, combine the measurement noise covariance, the covariance matrix and the observation matrix to calculate the Kalman filter gain K ω,t .

[0013] s5: Based on the obtained estimation error and Kalman filter gain, update the weights of the RNN network to obtain the predicted values of the lateral speed and yaw rate at the next time Meanwhile, update the covariance matrix.

[0014] s6: Construct the cost function so that the predicted lateral speed and yaw rate are as close to the ideal values as possible, and use the interior point method to optimize and solve to obtain the optimal solution δ of the predicted control fp * .

[0015] s7: According to the real-time lateral position error and yaw rate error of the vehicle, design a double PID controller to obtain the final output steering angle δ fb .

[0016] s8: Set the weight coefficient to obtain the final output steering angle δ f Complete the trajectory tracking control of the vehicle.

[0017] Further, the vehicle lateral speed v y And the yaw rate ω is obtained according to the mechanical analysis and Newton's second law, as follows:

[0018]

[0019] Where, denotes the lateral velocity rate of change of the vehicle, denotes the yaw rate of change, m is the mass of the vehicle, I z is the moment of inertia of the vehicle about the center of mass, l f and l r are the distances from the front and rear axles to the center of mass, F xf , F yf , F yr are the longitudinal force, lateral force of the front wheel, and lateral force of the rear wheel, respectively, subscript x denotes longitudinal, y denotes lateral, f denotes front wheel, and r denotes rear wheel;

[0020] After discretization of the mapping relationship, the state updates of v y and ω can be represented as:

[0021]

[0022] wherein denote the updated values of the vehicle lateral velocity and yaw rate at the next time, X t denotes the state quantity at time t, u t denotes the steering input at time t, Φ t (X t , u t ) denotes the feature vector, a high-dimensional feature extracted from the state and input through a nonlinear function, used to describe the nonlinear dynamic characteristics of the system, and W ω are the weight vectors of the lateral velocity and yaw rate, respectively, which are gradually updated through the learning process of the recurrent neural network to adapt to the nonlinear dynamic behavior of the vehicle.

[0023] Further, the activation function in S2 is defined as:

[0024]

[0025] wherein, denotes the predicted vehicle lateral speed at the previous time, denotes the predicted vehicle yaw rate at the previous time, v x,t denotes the current vehicle longitudinal speed, δ f,t denotes the current vehicle output steering angle, f act denotes the activation function, which takes the tanh function. Further, the characteristic polynomial ε t,i in S3 is as follows:

[0026]

[0027] wherein, superscript Ω 1,i denotes the first row of the i-th column of the corresponding matrix Ω, Ω i,2represents the 2nd row of the i-th column of the corresponding matrix Ω, Ω i,3 , Ω i,4 By analogy, different rows are represented; i is sequentially traversed from 1 to 15, and the high-dimensional feature vector ε t obtained has a dimension of 15.

[0028]

[0029] Further, the constructed observation matrix in S4 is as follows:

[0030]

[0031] wherein and H ω,t respectively represent the observation matrices of the lateral velocity and the yaw rate;

[0032] The filtering gain of the Kalman filter and K ω,t is updated as follows:

[0033]

[0034] wherein P ω,t respectively represent the covariance matrices of the lateral velocity and the yaw rate, and H ω,t represent the observation matrices, and R is the measurement noise covariance.

[0035] Further, in S5, the estimation error is constructed as follows:

[0036]

[0037] wherein, respectively represent the current sensor obtained lateral velocity and lateral angular velocity state measurement values;

[0038] Based on the obtained estimation error e ω,t and the filtering gain and K ω,t , the weight update of the neural network is performed:

[0039]

[0040] wherein, η represents the learning rate, controlling the amplitude of each step update, and respectively represent the updated lateral velocity and yaw rate weight matrices;

[0041] The update of the covariance matrix is as follows:

[0042]

[0043] wherein respectively represent the updated lateral velocity, yaw rate covariance matrix; Q represents the process noise covariance.

[0044] The update of the system state estimation is as follows:

[0045]

[0046] wherein respectively represent the predicted value of the lateral velocity, yaw rate at the next time.

[0047] Further, the cost function of S6 is designed as follows:

[0048]

[0049] wherein represent the ideal lateral velocity and yaw rate planned at the next time.

[0050] Further, the implementation of S7 includes:

[0051] Define the lateral position error e y and the yaw rate error e ω :

[0052]

[0053] wherein Y is the current lateral position of the vehicle, Y ref represents the expected lateral position of the vehicle, ω is the actual yaw rate of the vehicle, ω ref is the expected yaw rate;

[0054] Take the error of the two as the input quantity of the double PID controller, and get the final output steering angle δ fb of the feedback controller:

[0055]

[0056] wherein K p1 , K i1 , K d1 , K p2 , K i2 , K d2 respectively represent the proportional, integral, and derivative gains of the two PID controls, and the parameters α and β are used to adjust the weight of the two controllers to achieve the best control effect.

[0057] Further, in S8, δ f = κ1δ fp + κ2δ fb, and K1 and K2 represent the weight coefficients of the two controller outputs, respectively.

[0058] The present application also provides a technical solution: a vehicle trajectory tracking controller, which can execute the content of the above control method.

[0059] The beneficial effects of the present application are:

[0060] (1) The present application innovatively introduces the recurrent neural network (RNN) method, which fully utilizes its core advantages of capturing dynamic change rules in time series, modeling long-term dependencies, and having nonlinear mapping capabilities and network internal feature expression capabilities, thereby significantly improving the modeling capability of nonlinear coupling relationships between complex system states and control inputs. Through this improvement, the present application effectively solves the control accuracy and trajectory tracking performance problems of vehicle dynamics under complex working conditions (such as model mismatch), and exhibits significant superiority in the field of vehicle dynamics control.

[0061] (2) The synergistic effect of the predictive-feedback controller enables the system to maintain the efficiency of online predictive control while achieving more accurate and stable path tracking in complex environments. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is the overall framework diagram of the control method

[0063] Figure 2 is a schematic diagram of an online adaptive RNN prediction module

[0064] Figure 3 is a schematic diagram of a vehicle dynamics model DETAILED DESCRIPTION

[0065] In order to facilitate the understanding of those skilled in the art, the present application will be further described below in conjunction with the embodiments and the accompanying drawings. The content mentioned in the embodiments is not a limitation of the present application.

[0066] The overall framework of the control method of the present application is shown in Figure 1 , and Figure 2 is a schematic diagram of an online adaptive RNN prediction module (corresponding to steps 1 to 6). The control method comprises the following steps:

[0067] Step 1: As shown in Figure 3 , according to mechanical analysis and Newton's second law, the lateral velocity change rate and the yaw angular velocity change rate of the vehicle can be obtained.

[0068]

[0069] where m is the mass of the vehicle, Iz Iz, Iz f and Iz r are the distances from the front and rear axles to the center of mass, Fx xf , Fx yf , and Fy yr are the longitudinal force, lateral force of the front wheels, and lateral force of the rear wheels, which are affected by the tire characteristics of the vehicle, road conditions, and steering angle, and the system also has high nonlinear characteristics and parameter time-varying nature, making it difficult for model-based control strategies to adapt to the influence of complex dynamic conditions on path tracking performance. Therefore, the present application constructs a state equation to describe the vehicle dynamics based on the nonlinear mapping relationship of the vehicle:

[0070]

[0071] where X represents the state vector of the system, including the lateral velocity v y and yaw rate ω of the vehicle, and u represents the control input, i.e., the steering angle δ f of the front wheels.

[0072] A recurrent neural network (RNN) is also introduced to fit the nonlinear mapping of the system. In the discrete time framework, the state updates of the state variables v y and ω can be represented as:

[0073]

[0074] where v and ω represent the updated values of the lateral velocity and yaw rate of the vehicle at the next time, X t represents the state quantity at time t, and u t represents the steering angle input at that time t. The feature vector Φ t (X t , u t ) is usually extracted from the state and input through a nonlinear function to extract high-dimensional features to characterize the nonlinear dynamic characteristics of the system. and W ω are the weight vectors of the lateral velocity and yaw rate, which are gradually updated through the learning process of the recurrent neural network to adapt to the nonlinear dynamic behavior of the vehicle.

[0075] Step two: At each time step, the RNN network receives the predicted value of the state quantity at the previous time t the current longitudinal vehicle speed v x,t and the current control input of the system δ f,t , f actdenotes the activation function, which takes the tanh function. These feature quantities are normalized by the hyperbolic tangent activation function to ensure that all data is within a uniform numerical range, thereby avoiding instability and enhancing the convergence of the neural network. The specific activation function is defined as:

[0076]

[0077] Step three: Construct the characteristic polynomial ε t,i , which represents the polynomial combination of the state variables and front wheel steering angle δ f of the i-th layer network at time t:

[0078]

[0079] where Ω i,1 represents the first row of the i-th column of matrix Ω, Ω i,2 represents the second row of the i-th column of matrix Ω, Ω i,3 , Ω i,4 and so on, representing different rows; i is traversed from 1 to 15, resulting in a high-dimensional feature vector ε t with a dimension of 15.

[0080]

[0081] Through such feature expansion, the neural network can better fit the complex vehicle dynamics model, improving the accuracy of the model and the final control effect.

[0082] Step four: Construct the observation matrix by taking the transpose of the high-dimensional feature vector ε t , i.e. ε t T , i.e.:

[0083]

[0084] where and H ω,t represent the observation matrices of lateral velocity and yaw rate, respectively. This method can effectively reduce the computational complexity, while the polynomial expansion in the nonlinear feature expansion increases the observability of the system and the filtering effect. The filtering gain and K ω,t of the Kalman filter are updated as follows:

[0085]

[0086] where P ω,t represent the covariance matrices of lateral velocity and yaw rate, respectively, and H ω,tR is the measurement noise covariance.

[0087] Step five: Construct the estimation error of lateral velocity and lateral angular velocity e ω,t As a feedback signal, the neural network weight of the adaptive adjustment system:

[0088]

[0089] where Vx and Vy represent the current sensor obtained lateral velocity and lateral angular velocity state measurement.

[0090] Finally, based on the obtained estimation error e ω,t And filter gain And K ω,t , the weight update of the neural network:

[0091]

[0092] Where η represents the learning rate, which controls the amplitude of each step update. And Vx and Vy represent the updated lateral velocity and lateral angular velocity weight matrix.

[0093] At the same time, the covariance recursive update also reflects the process of the system's uncertainty gradually reducing the state estimation, as follows:

[0094]

[0095] Where Vx and Vy represent the updated lateral velocity and lateral angular velocity covariance matrix, and Q represents the process noise covariance. By combining the prediction uncertainty of the covariance matrix with the measurement update, the update controls the variance of the system estimation to ensure that the system gradually converges to a stable state. Finally, the update of the system state estimation is completed:

[0096]

[0097] Where Vx and Vy represent the predicted value of the lateral velocity and lateral angular velocity at the next time.

[0098] Step six: In the trajectory tracking control of vehicle dynamics, the goal of the system is to ensure that the state of the vehicle can be as close as possible to the predetermined ideal trajectory. To achieve this goal, the present invention defines a cost function J to measure the error between the predicted value of the state of the vehicle at the current time and the target state. By minimizing the cost function, the optimal control input can be found, so that the vehicle can be as close as possible to the target trajectory at the next time. The cost function J is constructed as follows:

[0099]

[0100] where represents the ideal lateral velocity and yaw rate at the next time (t+1 time). By minimizing J, the optimal solution of the predicted control amount δ fp * is obtained by using the interior point method, so that the vehicle state can be as close as possible to the target trajectory. At the same time, in order to further ensure the stability and safety of the system in real driving, the control amount of front wheel steering angle is limited during the solution process, which is guaranteed to be in a reasonable range, i.e.:

[0101]

[0102] where δ f,min and δ f,max represent the minimum and maximum front wheel steering angles allowed by the system, respectively.

[0103] Step seven: define the tracking lateral position error e y and yaw rate error e ω :

[0104]

[0105] where Y is the current lateral position of the vehicle, Y ref represents the desired lateral position of the vehicle. ω is the actual yaw rate of the vehicle, and ω ref is the desired yaw rate. By taking the error of the two as the input quantity of the double PID controller, the final output steering angle δ fb of the feedback controller is obtained:

[0106]

[0107] where K p1 , K i1 , K d1 , K p2 , K i2 , K d2 represent the proportional, integral and derivative gains of the two PID controllers, respectively. Parameters α and β are used to adjust the weights of the two controllers to achieve the best control effect, δ ey and δeω respectively represent the feedback angles generated based on the lateral deviation and the yaw rate deviation.

[0108] Step eight: combine the output results of the online adaptive RNN predictive controller and the double PID feedback controller, adjust the weight coefficients κ1 and κ2 of δ and δ fb , achieve the balance of the two, ensure stable trajectory tracking control, and obtain the final steering angle input:

[0109]

[0110] wherein κ1 and κ2 represent the weight coefficients of the outputs of the two controllers, for example, κ2 = 0.7 and κ2 = 0.3, and the optimal control effect is achieved by adjusting the two weights.

[0111] Based on the above control method, the embodiment of the present application further proposes a controller for vehicle trajectory tracking, which can execute the above method.

[0112] The above series of detailed descriptions are only specific descriptions of the feasible embodiments of the present application, and are not used to limit the protection scope of the present application. Any equivalent means or changes without departing from the technology of the present application shall be included in the protection scope of the present application.

Claims

1. An adaptive RNN vehicle trajectory tracking control method based on online learning, characterized in that, The method comprises the following steps: S1: Nonlinear mapping relation based on vehicle The state equation is constructed to describe the vehicle dynamics, where X represents the state vector of the system, including the lateral velocity v y and the yaw rate ω of the vehicle, and u represents the control input, i.e. the front wheel steering angle δ f , and the mapping relation is discretized; S2: fitting a nonlinear mapping of the system based on a recurrent neural network, receiving at each time step a prediction of the state quantity from the previous time instant the longitudinal vehicle speed v at the current time instant x,t and the current control input of the system δ f,t and normalizing it by an activation function; S3: Constructing feature polynomial ε t,i , represents the i-th layer network at time t by the state variable current longitudinal speed v x,t , the last time predicted lateral speed The last time predicted yaw rate And the current front wheel angle δ f Construct a high-dimensional feature vector ε t , the dimension of the feature vector is the number of RNN network layers; S4: Constructing an observation matrix based on the high-dimensional feature vector, and combining the measurement noise covariance, the covariance matrix and the observation matrix to update the Kalman filter gain K ω,t ; S5: weight updating of the RNN network based on the estimation error and the Kalman filter gain, to obtain the predicted value of the lateral velocity and the yaw rate at the next time At the same time, the covariance matrix is updated, and the update of the system state estimation is completed. S6: Construct a cost function so that the predicted lateral velocity and yaw rate are as close to the ideal values as possible, and use the interior point method to solve the optimization to obtain the optimal solution of the predicted control variable δ fp * ; S7: Design a double PID controller according to the lateral position error and the yaw rate error of the vehicle in real time to obtain the final output steering angle δ fb ; S8: Set the weight coefficient to obtain the final output steering angle δ f , complete the trajectory tracking control of the vehicle. 2.The online learning based adaptive RNN vehicle trajectory tracking control method according to claim 1, characterized in that, The vehicle lateral velocity v of the S1 y And the yaw rate ω is obtained according to the mechanical analysis and Newton's second law, as follows: wherein, represents a lateral velocity change rate of the vehicle, represents a yaw angular velocity change rate, m is a mass of the vehicle, I z is a moment of inertia of the vehicle about the center of mass, l f and l r are distances from the front and rear axles to the center of mass, respectively, F xf , F yf , F yr are longitudinal, lateral and lateral forces of the front and rear wheels, respectively, subscript x represents longitudinal, y represents lateral, f represents the front wheel, and r represents the rear wheel; After discretization of the mapping relationship, the state variable v y The state updates of v and ω can be expressed as follows, respectively: where denote the vehicle lateral velocity and yaw rate update values at the next time instant, X t denote the state quantities at time t, u t denote the steering angle input at time t, Φ t (X t , u t ) denote the feature vector, a high-dimensional feature extracted from the state and input through a nonlinear function, used to describe the nonlinear dynamic characteristics of the system, and W ω are the weight vectors for lateral velocity and yaw rate, respectively, updated step by step through the learning process of the recurrent neural network to adapt to the nonlinear dynamic behavior of the vehicle. 3.The online learning based adaptive RNN vehicle trajectory tracking control method according to claim 2, characterized in that, The activation function in S2 is defined as: where v x,t denotes the longitudinal vehicle speed at the current time, denotes the lateral vehicle speed predicted at the previous time, denotes the yaw rate predicted at the previous time, δ f,t denotes the front wheel angle at the current time, f act denotes the activation function, which takes the tanh function. 4.The online learning based adaptive RNN vehicle trajectory tracking control method of claim 3, wherein, The characteristic polynomial ε in S3 t,i In detail as follows: where Ω i,1 represents the first row of the i-th column of the following matrix Ω i,2 represents the second row of the i-th column of the matrix Ω i,3 , Ω i,4 and so on for different rows; i runs from 1 to 15, resulting in a high-dimensional eigenvector ε t with dimension 15, 5. The adaptive RNN vehicle trajectory tracking control method based on online learning according to claim 4, characterized in that, The observation matrix constructed in S4 is as follows: wherein and H ω,t and H represent the observation matrix of lateral velocity and yaw rate, respectively; Filtering gain of Kalman filter and K ω,t The update is as follows: wherein P ω,t respectively denote the cross-covariance matrix of lateral velocity and yaw rate, and H ω,t denotes the observation matrix, and R is the measurement noise covariance. 6.The online learning based adaptive RNN vehicle trajectory tracking control method according to claim 4, characterized in that, In S5, the estimation error is constructed as follows: wherein, respectively denote the lateral velocity and lateral angular velocity state measurement values obtained by the current sensor; based on the resulting estimation error e ω,t and a filter gain and K ω,t weight update of the neural network: wherein η denotes a learning rate, controls the magnitude of the update at each step, and denote the weight matrices for the updated lateral velocity and yaw rate, respectively. The update of the covariance matrix is as follows: wherein respectively denote the updated cross velocity, yaw rate covariance matrices; Q denotes the process noise covariance; The update of the system state quantity estimation is as follows: wherein respectively denote the predicted values of lateral velocity, yaw rate at next time.

7. The adaptive RNN vehicle trajectory tracking control method based on online learning according to claim 6, characterized in that, The cost function design of S6 is as follows: wherein denotes the ideal lateral velocity and yaw rate planned for the next time instant. 8.The online learning based adaptive RNN vehicle trajectory tracking control method of claim 1, wherein, The implementation of S7 comprises: defining a lateral position error e y and a yaw angular velocity error e ω : where Y is the current lateral position of the vehicle, Y ref represents the desired lateral position of the vehicle, ω is the actual yaw rate of the vehicle, ω ref is the desired yaw rate; The error of both is taken as the input quantity of the double PID controller, and the final output rotation angle δ of the feedback controller is obtained fb : Where K p1 K i1 K d1 K p2 K i2 K d2 These represent the proportional, integral, and derivative gains of the two PID controllers, respectively. Parameters α and β are used to adjust the weights of the two controllers to achieve the best control effect. 9.The online learning based adaptive RNN vehicle trajectory tracking control method of claim 1, wherein, In S8, δ f = κ1δ fp + κ2δ fb , κ1 and κ2 represent weight coefficients of the two controller outputs, respectively.

10. A vehicle trajectory tracking controller, characterized by, The controller can perform the adaptive RNN vehicle trajectory tracking control method based on online learning according to any one of claims 1-9.

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